Suppose Cournot duopolist firms operate with each having a cost of 30q_i (i = 1,2)so that each firm's marginal cost is 30.The inverse market demand curve is P = 120 - Q where Q = q₁ + q₂.At the Nash-Cournot equilibrium,the market price,P,is

Question

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At the Nash-Cournot equilibrium, each firm maximizes its profits by choosing its quantity given the quantity of other firm's output. This can be found by solving the following equations for both firms:

MR = MC

Where MR is the marginal revenue and MC is the marginal cost.

The market demand can be written as: P = 120 - Q
where Q = q1 + q2

By differentiating the above equation with respect to q1, we get:

MR1 =  120 - 2q1 - q2

Setting this equal to MC1 = 30, we get:

q1 = (90 - q2)/2

Similarly, we can solve for q2:

q2 = (90 - q1)/2

Substituting these values back into the expression for Q, we get:

Q = q1 + q2 = 90/2 = 45

Therefore, the market price is:

P = 120 - Q = 75

So, none of the answer choices are correct. However, the closest choice is C) 60.

Suppose Cournot Duopolist Firms Operate with Each Having a Cost